To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

a(a - x)
1(-4)(-4 - 1)
1(-4)(-5)
(-4)(-5)
20

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with c° = 19, the value of b° is 161.

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

b² - 4 = 0
(b - 2)(b + 2) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 2) or (b + 2) must equal zero:

If (b - 2) = 0, b must equal 2
If (b + 2) = 0, b must equal -2

So the solution is that b = 2 or -2